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This is supposed to work, assuming you meant a symlink from and not a into the original location. Something like

ln -sf /var/rancher-desktop /home/<ME>/.local/share/rancher-desktop

Yes, that's what I did. Yes, the symlink worked properly. I wonder if I needed to change the permissions on all of the parent folders, they were 0755 root:root. I'll try again and report back.

The permission for the parent folders sound fine (you just need execute permission to traverse them), but the moved directory still needs to be owned by your current user.